7 research outputs found
Resolutions and Characters of Irreducible Representations of the N=2 Superconformal Algebra
We evaluate characters of irreducible representations of the N=2
supersymmetric extension of the Virasoro algebra. We do so by deriving the
BGG-resolution of the admissible N=2 representations and also a new
3,5,7...-resolution in terms of twisted massive Verma modules. We analyse how
the characters behave under the automorphisms of the algebra, whose most
significant part is the spectral flow transformations. The possibility to
express the characters in terms of theta functions is determined by their
behaviour under the spectral flow. We also derive the identity expressing every
character as a linear combination of spectral-flow transformed
N=2 characters; this identity involves a finite number of N=2 characters in the
case of unitary representations. Conversely, we find an integral representation
for the admissible N=2 characters as contour integrals of admissible
characters.Comment: LaTeX2e: amsart, 34pp. An overall sign error corrected in (4.33) and
several consequent formulas, and the presentation streamlined in Sec.4.2.3.
References added. To appear in Nucl. Phys.
Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
We introduce a Kazhdan--Lusztig-dual quantum group for (1,p) Virasoro
logarithmic minimal models as the Lusztig limit of the quantum sl(2) at pth
root of unity and show that this limit is a Hopf algebra. We calculate tensor
products of irreducible and projective representations of the quantum group and
show that these tensor products coincide with the fusion of irreducible and
logarithmic modules in the (1,p) Virasoro logarithmic minimal models.Comment: 19 page
Logarithmic extensions of minimal models: characters and modular transformations
We study logarithmic conformal field models that extend the (p,q) Virasoro
minimal models. For coprime positive integers and , the model is defined
as the kernel of the two minimal-model screening operators. We identify the
field content, construct the W-algebra W(p,q) that is the model symmetry (the
maximal local algebra in the kernel), describe its irreducible modules, and
find their characters. We then derive the SL(2,Z) representation on the space
of torus amplitudes and study its properties. From the action of the
screenings, we also identify the quantum group that is Kazhdan--Lusztig-dual to
the logarithmic model.Comment: 43pp., AMSLaTeX++. V3: Some explanatory comments added, notational
inaccuracies corrected, references adde
Logarithmic Conformal Field Theories via Logarithmic Deformations
We construct logarithmic conformal field theories starting from an ordinary
conformal field theory -- with a chiral algebra C and the corresponding space
of states V -- via a two-step construction: i) deforming the chiral algebra
representation on V\tensor End K[[z,1/z]], where K is an auxiliary
finite-dimensional vector space, and ii) extending C by operators corresponding
to the endomorphisms End K. For K=C^2, with End K being the two-dimensional
Clifford algebra, our construction results in extending C by an operator that
can be thought of as \partial^{-1}E, where \oint E is a fermionic screening.
This covers the (2,p) Virasoro minimal models as well as the sl(2) WZW theory.Comment: LaTeX, 35 pages, 4 eps figures. v2: references adde
Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
The subject of our study is the Kazhdan-Lusztig (KL) equivalence in the
context of a one-parameter family of logarithmic CFTs based on Virasoro
symmetry with the (1,p) central charge. All finite-dimensional indecomposable
modules of the KL-dual quantum group - the "full" Lusztig quantum sl(2) at the
root of unity - are explicitly described. These are exhausted by projective
modules and four series of modules that have a functorial correspondence with
any quotient or a submodule of Feigin-Fuchs modules over the Virasoro algebra.
Our main result includes calculation of tensor products of any pair of the
indecomposable modules. Based on the Kazhdan-Lusztig equivalence between
quantum groups and vertex-operator algebras, fusion rules of Kac modules over
the Virasoro algebra in the (1,p) LCFT models are conjectured.Comment: 40pp. V2: a new introduction, corrected typos, some explanatory
comments added, references adde